Lossless and near-lossless image and video compression techniques have generated considerable interest in the video processing community in recent years. Examples of such known techniques have been extensively described in the image and video compression literature, for example: Draft of MPEG-2: Test Model 5, ISO/IEC JTC1/SC29/WG11, April 1993; Draft of ITU-T Recommendation H.263, ITU-T SG XV, December 1995; “Lossless and near-lossless coding of continuous tone still images” (JPEG-LS), ISO/IEC JTC1/SC 29/WG 1, July 1997; B. Haskell, A. Puri, and A. N. Netravali, “Digital video: An introduction to MPEG-2,” Chapman and Hall, 1997; H. G. Musmann, P. Pirsch, and H. J. Gralleer, “Advances in picture coding,” Proc. IEEE, vol. 73, no. 4, pp. 523-548, April 1985; N. D. Memon and K. Sayood, “Lossless compression of video sequences,” IEEE Trans. Communications, vol. 44, no. 10, pp. 1340-1345, October 1996; A. N. Netravali and B. G. Haskell, “Digital Pictures: Representation, Compression, and Standards,” 2nd Ed., Plenum Press, 1995; W. Philips and K. Denecker, “A Lossless Version of the Hadamard Transform,” Proc. ProRISC Workshop on Circuits, Systems and Signal Processing, pp. 387-392, 1997; A. Said and W. A. Pearlman, “New, fast, and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. Circuit and Systems for Video Technology, vol. 6, no. 3, pp. 243-249, June 1996; M. J. Weinberger, J. J. Rissanen, and R. B. Arps, “Applications of universal context modeling to lossless compression of gray-scale images,” IEEE Trans. Image Processing, vol. 5, no. 4, pp. 575-586, April 1996; X. Wu and N. Memon, “Context-based, adaptive, lossless image coding,” IEEE Trans. Communications, vol. 45, no. 4, pp. 437-444, April 1997; and Z. Xiong, K. Ramchandran, and M. T. Orchard, “Space frequency quantization for wavelet image coding,” IEEE Trans. Image Processing, vol. 6, 1997.
These conventional techniques have been used in an attempt to generate high quality, perceptually distortion free compressed video and still images. One of the issues of interest in lossy coding is one-time coding loss or lossless-concatenated coding, where repeated encoding and decoding of a signal does not introduce errors beyond the quantization error added during the original encoding process. Certain applications involving high quality, perceptually distortion free compressed video or still images require such repeated encoding and decoding operations. For instance, in the case where such originally encoded signals are archived on a storage device for some period of time, it may be desirable to periodically decode the stored video or images, check the video or images current quality, and then encode it again for storage back on the same or a different storage device. This may be done because of the potential for degradation of the storage device over time, which thus causes a degradation in the quality of the video or images. Also, by way of further example, in the case where the archived video or images are to be edited (e.g., mix, fade, etc), possibly with other signals, the stored information may be decoded each time such that it may be forwarded to an editing facility. The decoded and edited information is then encoded again and returned to the storage device. In any case, a major concern is that such repeated encoding and decoding of the video or images does not introduce errors beyond the quantization error added during the original encoding process.
Context-based coding techniques have been considered in this light, where the status of both the encoder and decoder at any point during the encoding/decoding process is solely determined by the previously reconstructed samples. Repeated encoding/decoding using the same coding parameters thus produced identical bit streams, resulting in lossless-concatenated coding. Context-based coding approaches which have attempted to take this issue into consideration can be roughly classified into two categories: context-based predictive coding in the spatial domain and context-based coding in the wavelet domain. Examples of the spatial domain techniques are discussed in “Lossless and near-lossless coding of continuous tone still images” (JPEG-LS), ISO/IEC JTC1/SC 29/WG 1, July 1997; the Weinberger et al. article; and the Wu et al. article, as mentioned above. Examples of the wavelet domain techniques are discussed in the Memon et al. article; the Said et al. article; and the Xiong et al. article, as mentioned above.
Unfortunately, lossy block transform coding schemes do not exhibit the above property, as will be explained below. Accordingly, it would be highly advantageous to provide a transform-based coding technique, where the coding loss introduced during repeated encoding and decoding is reduced to a substantially insignificant level.